We report the design, simulation, and fabrication of a single-mode red semiconductor laser featuring a near-circular beam spot, tailored for near-eye display applications with demands on single-mode operation and high resolution. The near- and far-field distributions of eigenmodes were analyzed to optimize epitaxial structure and ridge waveguide. Conditions required for stable single-mode operation as well as strategies for divergence angle control were theoretically established. Prototype devices were subsequently fabricated to validate the design. The realized laser exhibits robust single-mode operation with an output power of 235 mW and a threshold current of approximately 51 mA. Near-circular beam demonstrates fast- and slow-axis divergence angles of 13.6° and 9.5°, respectively, fulfilling the single-mode operation and high resolution requirements of near-eye display systems and providing critical support for their further development.